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Dimitri Zaganidis "On a (∞,2)-category of homotopy coherent adjunctions in an ∞-cosmos.'"

Start Date:

4/16/2018

Start Time:

4:30 PM

End Date:

4/16/2018

End Time:

5:30 PM

Event Description:Speaker: Dimitri Zaganidis, EPFL

Abstract: Riehl and Verity initiated a program to study the category theory of (∞,1)-categories in a model-independent way, through the study of ∞-cosmoi. Homotopy coherent monads in an ∞

-cosmos are of particular interest since they determine an Eilenberg-Moore object of (homotopy coherent) algebras.

In this talk, I will generalize the graphical calculus of Riehl and Verity to provide a combinatorial description of the simplicial categories Adjhc[n]and Mndhc[n]. They encode homotopy coherent diagrams of homotopy coherent adjunctions and monads of the shape of the simplex Δ[n], and in particular for n=1

I will briefly introduce weak complicial sets and show that the nerve induced by Adjhc[−]:Δ→sSet−Catgives rise to an (∞,2)-category of homotopy coherent adjunctions. If time permits, I will discuss a related conjecture for homotopy coherent monads.